The role of connectivity in the properties of sedimented materials

Effective-medium theories for both random packings of elastic discs and mats of randomly sedimented elastic fibers can be constructed such that the effective material stiffness depends on the stiffness and geometry of the constituents of the material, and the number density of contacts. It is demonstrated that the number density of contacts together with the geometry of the constituents also determine the porosity of these materials. The simplicity and similar structure of the effective-medium estimates for the properties of these two qualitatively different materials indicate that the number density of contacts may play a similar role in an appropriate effective-medium description of a large class of materials formed by processes similar to random deposition. A simple method to determine the density of contacts and the fraction of bonded contacts by two macroscopic measurements for materials that belong to this class is suggested.